An arbitration system receives requests to access a destination during an arbitration window that spans multiple processor clock cycles. During each clock cycle, the destination is monitored to determine whether the destination is suffering from backpressure by receiving more requests than the destination is able to accommodate during the clock cycle. In response to detecting backpressure, a masking index value assigned to a requesting source is incremented, which limits an amount of requests from the source that will be granted destination access during a subsequent arbitration window. Alternatively, in response to detecting an absence of backpressure during an arbitration window, the masking index value is decremented, which increases the amount of requests from the source that will be granted destination access during a subsequent arbitration window. This arbitration process continues for successive arbitration windows, oscillating between incrementing and decrementing the masking index value during the successive arbitration windows.